For each of the following sets of data, do the following: determine the independent (x) and dependent (y) variables assume a causal ('cause-and-effect') relationship using technology*, create a scatter plot with a 'line of best fit' using technology*, perform regression analysis in order to find: the linear model (equation) the coefficient of determination / variance (R2) the correlation coefficient (r) use the linear model (equation) you find to answer the question (for that set of data) discuss how 'good' the models (linear equation, 'line of best fit') fit the data, usingappropriate math language and tools.* you may use any of the technology options suggested in U3A2: Regression Analysis and Correlation Coefficient - just ensure that I know which one(s) you are using for this test!IMPORTANT! There was a question missing from the original -- please make these corrections:Question #2change c) to d)Add #2c) "An outlier is a point that doesn't 'fit' with the rest of the data. While you shouldn't normally 'mess' with your data, sometimes you might want to remove outliers (with explanation) in order to see the results (especially for a small sample size, like this one, where an outliner may have a significant effect). Remove the outlier in this set of data, and analyze the data again (repeat part a). Do you notice a change in the correlation between the variables?"3. 3. Height vs Arm Span. According to Leonardo da Vinci, the ideal dimensions of a human are when their height equalled their arm span (as shown by the Vitruvian Man drawing, at right). Note that this is NOT a causal relationship, so we will simply let x be height and y be arm span.a) You will be collecting data from an online database called Census at School, compiled by students from all around the world. Here is how you get your data:i. go to censusatschool.caii. on the right hand side, click on Data and Resultsiii. at the bottom of the page, click on the link to the NewZealand sampler (NOT the American sampler)iv. click the I AGREE boxv. select a sample size of 100, then click the Get my samplebuttonvi. click Download sample button this will download a.CSV file (which can be opened by Microsoft Excel, OpenOffice Calc, or other major spreadsheet programs)b) After downloading the data, either select only the data you want (height, arm span), or 'copy- and-paste' the desired data into your chosen technology. Note that everybody's data will be different! If there are any values that are OBVIOUSLY wrong, you will need to delete BOTH values.c) Analyze the data (as described on the previous page). There is NO way you can do these calculations by hand, with 100 data points!d) Is there a relationship between height and arm span? Use mathematical tools and measures in your answer.

1. Universities rate high schools by comparing a student's 1st year university average with the student's average in their top 6 Grade 12 courses. Here is some recent data: -Il [Hamlin-\"Ella: WEE] a) Analyze the data {as above). b) Predict the University Average of a student who had a 60 for their High School Average. 2. Mr. Elliott wants to investigate if student performance on the MDM4U final exam is related to time spent studying for the exam. He gathered the following sample data: mum \"mammal a) Analyze the data {as above). b) Predict the exam mark of a student who studied for 30 hours. c) Is this model a fair way to predict success in MDM4U exam? Use mathematical reasoning, not your personal feelings